Best way to craft custom command with 4 optional arguments

Question

I would like to make a command that produces the following results

\myquantity[Q]
\myquantity[Q][i]
\myquantity[Q][][j]
\myquantity[Q][i][j]
\myquantity[Q][i][j][\bar]
\myquantity[Q][][][\bar]
\myquantity[Q][][][\tilde]
\myquantity[Q_c][i][j][\bar]

My current solution is the following

\newcommandx{\myquantity}[4][1=, 2=, 3=, 4=]{
  \des[#4]{#1}{#3}(\lambda_{#2})}  

where \des is the command in the supplement of this answer.

Is there a simpler way to obtain the same result?

Answer 1

I would like to argue that having four optional arguments is not very semantic. I would use a command with a key=value optional argument.

\myquantity[Q_c][i][j][\bar]

is a lot less readable than

\myquantity[accent=\bar,subscript={c,j},lambda subscript=i]{Q}

although the latter might be using a bit too long keys, I hope you agree it is easier to understand.

The following MWE gives an example of your desired command, using a key-value argument. If you indeed think the keys are too long, you can always change them what you find descriptive enough.

\documentclass{article}

\usepackage{amsmath}
\usepackage{pgf}

\makeatletter
\newif\if@myquantity@subscript
\newif\if@myquantity@lambdasubscript
\pgfkeys{
    my quantity/.cd,
        accent/.code={\let\@myquantity@accent#1},
        accent=\relax,
        subscript/.code={\def\@myquantity@subscript{#1}\@myquantity@subscripttrue},
        lambda subscript/.code={\def\@myquantity@lambdasubscript{#1}\@myquantity@lambdasubscripttrue},
}
\newcommand{\myquantity}[2][]{%
    \@myquantity@subscriptfalse
    \@myquantity@lambdasubscriptfalse
    \pgfkeys{my quantity/.cd,#1}%
    \if@myquantity@subscript%
        \@myquantity@accent{#2}_{\@myquantity@subscript}%
    \else%
        \@myquantity@accent{\mathbf{#2}}%
    \fi%
    (\lambda%
    \if@myquantity@lambdasubscript
        _{\@myquantity@lambdasubscript}%
    \fi)%
}
\makeatother

\begin{document}
    \begin{equation*}
        \begin{array}{lll}
            \myquantity{Q} &
            \myquantity[lambda subscript=i]{Q} &
            \myquantity[subscript=j]{Q}\\
            \myquantity[subscript=j,lambda subscript=i]{Q} &
            \myquantity[accent=\bar,subscript=j,lambda subscript=i]{Q} &
            \myquantity[accent=\bar]{Q} \\
            \myquantity[accent=\tilde]{Q} &
            \myquantity[accent=\bar,subscript={c,j},lambda subscript=i]{Q}
        \end{array}
    \end{equation*}
\end{document}

Resulting in

Answer 2

Four optional arguments require too much care in input. Besides, one of them is mandatory and the last one refers to the mandatory argument, so it should be specified first.

My idea is

\myq[<optional decoration>]{<variable>}[<optional coordinate>](<optional subscript)

so there is no need to specify empty optional arguments.

What do the macros do? First I look for _ in the optional argument, because this should not be part of \mathbf when no coordinate appears. For this purpose, \regex_split:nnN is available: if no _ is found, the sequence will have just one item, otherwise it will have two (what comes before _ and what comes after).

Then it's a matter of checking whether the coordinate is specified, in order to decide for \mathbf or not.

The <decoration> should be a math accent command; it defaults to \use:n, which means “output the argument” (the classical \@firstofone).

\documentclass{article}
\usepackage[leqno,fleqn]{amsmath} % the options are just to better show the output
\usepackage{xparse}

\ExplSyntaxOn

\NewDocumentCommand{\myq}{
  O{\use:n} % decoration for the main variable
  m         % main variable
  o         % coordinate
  d()       % subscript to \lambda
 }
 {
  % separate off the possible subscript to the variable;
  % item 1 contains the variable, item 2 the subscript
  \regex_split:nnN { \cD_ } { #2 } \l_simone_myq_var_seq
  % make the subscript
  \int_compare:nTF { \seq_count:N \l_simone_myq_var_seq = 1 }
   {% no subscript in #2
    \IfNoValueTF{#3}
     { #1 { \mathbf{#2} } }
     { #1 { #2 } \sb { #3 } }
   }
   {% subscript in #2
    \IfNoValueTF{#3}
     {
      #1 { \mathbf{\seq_item:Nn \l_simone_myq_var_seq { 1 }} } % base
      \sb { \seq_item:Nn \l_simone_myq_var_seq { 2 } }
     }
     {
      #1 { \seq_item:Nn \l_simone_myq_var_seq { 1 } } % base
      \sb { \seq_item:Nn \l_simone_myq_var_seq { 2 } , #3 }
     }
   }
  ( \lambda\IfValueT{#4}{\sb{#4}} )
 }

\seq_new:N \l_simone_myq_var_seq

\ExplSyntaxOff

\begin{document}

\begin{gather}
\myq{Q} \\
\myq[\bar]{Q} \\
\myq{Q}[i] \\
\myq{Q}(j) \\
\myq{Q}[i](j) \\
\myq[\tilde]{Q}(j) \\
\myq[\tilde]{Q}[i](j) \\
\myq{Q_c} \\
\myq[\bar]{Q_c} \\
\myq{Q_c}[i] \\
\myq{Q_c}(j) \\
\myq{Q_c}[i](j) \\
\myq[\tilde]{Q_c}(j) \\
\myq[\tilde]{Q_c}[i](j)
\end{gather}

\end{document}